Domain and Range
Have you ever wondered what causes a hailstorm vs what causes a snowstorm?
Standard(s) Supported: HSF.IF.A.1
Review: What is an input or output value? An input value is the value that goes into the relationship. An output value is the value created by the input value and the relationship.
What is domain and range?
Domain in math is the set of all possible input values for a given relationship. Many times, the input values are represented with the variable, x.
What is domain.pdfRange in math is the set of all possible output values for a given relationship. Many times, the output values are represented with the variable, y.
What is range.pdfSomething to always remember is that the range depends on the domain. An easy way to visualize this concept is to look at a restricted domain (or section of a domain) and then look at the range that depends on that restricted domain:
Range depends on domain.pdfWhat is a relationship in math? In math there are two types of relationships: Functions and Relations (non-functions). To review and explore functions and relations, check out the fundamental: Functions!
How do you write the domain and range ?
You may have noticed above that there are different ways to write out the domain and range of a given relationship. First, make sure you check with your current teacher to see how they typically write out the domain and range. Second, let’s take a quick moment to look at some different notations (ways to write) the domain and range of a relationship:
Notation Table.pdfHow do you indentify the domain and range of a relationship?
Domain and Range of Linear Relationships and Functions
Domain and Range of Linear Relationships and Functions.pdfDomain and Range of Linear Relationships and Functions Extension: Digging in Deeper
Domain and Range of a Linear Relationship and Function Extension.pdfWhat about a real-world linear situation? Does the domain and range for the equation model the actual real-world situation? To investigate domain and range in math problem solving check out the fundamental Problem Solving: Domain and Range (coming soon)!
Domain and Range of Quadratic Functions
Domain and Range of Quadratic Functions.pdfThe second question will be discussed more in the upcoming fundamental, Inverse Functions (coming soon), but for now a simple, NO, the inverse of a quadratic function is not a function.
Why do we learn about domain and range?
The business, tech, and science industries are constantly presented with new collections of data that need to be interpreted. Many times, the data set collected will not fit an entire function. However, part of a function may best represent the collected data set. In these cases, it would not make sense to use the entire possible domain but only the restricted domain that applies to the part of the function that best represents the collected data set. By focusing on a restricted domain, you can then learn about possible outcomes for the data set and these outcomes are the range of the function that are determined by the restricted domain. For instance, if a business is collecting data on sweater sales, it would make most sense to focus only on the domain that included cold weather months. The corresponding range could help the business make predictions about consumer demands for the next cold weather season.
What’s next? How can you use and/or define the domain and range when problem solving? Check out the fundamental, Problem Solving: Domain and Range (coming soon)!
